Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
An approximate method for numerical solution of fractional differential equations
Signal Processing - Fractional calculus applications in signals and systems
Numerical analysis for distributed-order differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
On the convergence of spline collocation methods for solving fractional differential equations
Journal of Computational and Applied Mathematics
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We investigate strategies for the numerical solution of the initial value problem y(αv)(x) = f(x, y(x), y(α1)(x),..., y(αv-1)(x)) with initial conditions y(k)(0) = y0(k) (k = 0, 1,..., ⌈αv⌉ - 1), where 0 1 2 v. Here y(xj) denotes the derivative of order αj 0 (not necessarily αj ∈ N) in the sense of Caputo. The methods are based on numerical integration techniques applied to an equivalent nonlinear and weakly singular Volterra integral equation. The classical approach leads to an algorithm with very high arithmetic complexity. Therefore we derive an alternative that leads to lower complexity without sacrificing too much precision.